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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 294 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.How many whole numbers lie between 31² and 32²?
  2. 2.Which of these is a perfect square? (a) 231 (b) 240 (c) 225
  3. 3.What is 85²? =
  4. 4.What is 51²? =
  5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  6. 6.A square garden has an area of 900 square m. How long is each side (in m)?
  7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  8. 8.Which of these is a perfect square? (a) 324 (b) 331 (c) 332
  9. 9.How many whole numbers lie between 26² and 27²?
  10. 10.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  11. 11.A square garden has an area of 100 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 2025 square m. How long is each side (in m)?
  13. 13.A square garden has an area of 2500 square m. How long is each side (in m)?
  14. 14.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
  15. 15.What is √676? =
  16. 16.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  17. 17.How many whole numbers lie between 36² and 37²?
  18. 18.Which of these is a perfect square? (a) 1521 (b) 1582 (c) 1557
  19. 19.A square garden has an area of 441 square m. How long is each side (in m)?
  20. 20.What is the smallest whole number by which 294 must be divided to get a perfect square?
  21. 21.What is √2916? =
  22. 22.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  23. 23.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 34² and 35²?
  25. 25.What is √8649? =
  26. 26.What is √3969? =
  27. 27.A square garden has an area of 2809 square m. How long is each side (in m)?
  28. 28.What is √6889? =
  29. 29.Which of these is a perfect square? (a) 1089 (b) 1138 (c) 1107
  30. 30.What is √7921? =
  31. 31.Which of these is a perfect square? (a) 841 (b) 875 (c) 889
  32. 32.What is the smallest whole number by which 250 must be divided to get a perfect square?
  33. 33.What is √2704? =
  34. 34.What is √841? =
  35. 35.What is 11²? =
  36. 36.Which of these is a perfect square? (a) 121 (b) 130 (c) 140
  37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  38. 38.A square garden has an area of 2916 square m. How long is each side (in m)?
  39. 39.What is 97²? =
  40. 40.What is √2304? =

Answer key

  1. 62
  2. 225
  3. 7225
  4. 2601
  5. 441
  6. 30
  7. 289
  8. 324
  9. 52
  10. 2
  11. 10
  12. 45
  13. 50
  14. 5
  15. 26
  16. 15
  17. 72
  18. 1521
  19. 21
  20. 6
  21. 54
  22. 3
  23. 169
  24. 68
  25. 93
  26. 63
  27. 53
  28. 83
  29. 1089
  30. 89
  31. 841
  32. 10
  33. 52
  34. 29
  35. 121
  36. 121
  37. 484
  38. 54
  39. 9409
  40. 48

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